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Thread engagement length calculator

How far must a bolt or screw be threaded into a nut or tapped hole so that the threads do not strip before the bolt breaks? Pick the thread, the bolt strength and the material of the tapped part and get the minimum engagement length for each thread, the governing one, and a drill-depth allowance. Inch or metric. Free, no sign-up, runs in your browser.

Minimum engagement

-- × nominal diameter

Governing thread

-The thread that strips first

Tapped hole depth

-Engagement plus 3 pitches (allowance)

Results

Tensile stress area At-
Bolt tensile capacity (At·Su)-
Design load used-
Minor diameter of internal thread D1-
Min. engagement, bolt threads-
Min. engagement, internal threads-
Bolt thread strip load at your engagement-
Internal thread strip load at your engagement-
Margin of weakest strip load over design load-

Checks

How the calculator works

The calculator finds the engagement length at which the shear strength of the engaged threads equals the load. It treats the threads as ISO or Unified basic profiles and assumes the load is shared evenly along the engagement.

  1. Thread data. Pitch P is the table value for metric threads and 1/n for UN threads. The tensile stress area is At = π/4·(d − 0.9382P)2 for metric threads and π/4·(d − 0.9743P)2 for UN threads. The basic minor diameter of the internal thread is D1 = d − 1.0825P.
  2. Load. Either the full tensile capacity of the bolt, F = At·Su,bolt, or an applied load you enter, multiplied by the safety factor.
  3. Shear areas. The bolt threads shear on the cylinder of diameter D1, where the basic bolt thread is 0.75P wide: Abolt = π·D1·0.75·Le. The internal threads shear on the cylinder of diameter d, where the basic internal thread is 0.875P wide: Aint = π·d·0.875·Le.
  4. Shear strength. τ = 0.6·Su for each material, a common estimate for ductile metals.
  5. Required engagement. Le,bolt = F / (0.6·Su,bolt·π·D1·0.75) and Le,int = F / (0.6·Su,part·π·d·0.875). The larger of the two governs.

When the load is the full capacity of the bolt, the bolt-thread value does not depend on the bolt grade, because the bolt strength cancels out. A stronger bolt only needs a longer engagement in the tapped part, so a class 12.9 screw in aluminium needs a lot of engagement. Material strengths are typical minimum tensile values; use the certified values of your material.

Worked example: M10 class 8.8 bolt in 6061-T6 aluminium

Thread M10×1.5: At = π/4·(10 − 1.407)2 = 58.0 mm² and D1 = 10 − 1.624 = 8.376 mm. The class 8.8 bolt has Su = 800 MPa, so the full capacity is 58.0 × 800 = 46.4 kN. Bolt threads: Le = 46391 / (0.6·800·π·8.376·0.75) = 4.9 mm. Internal threads in 6061-T6 (Su = 310 MPa): Le = 46391 / (0.6·310·π·10·0.875) = 9.1 mm. The aluminium threads govern: about 0.9 d, so a practical specification with margin is 1.5 to 2 d (15 to 20 mm). For a blind tapped hole add about 3 pitches (4.5 mm) of drill depth.

Size the rest of the joint

Thread engagement only checks stripping. Get the tightening torque and preload with the bolt torque calculator, and check the keys and fits around it.

Bolt torqueLimits and fitsKey and keyway

Questions

How much thread engagement do I need?

It depends on the strength of the weaker material. As a screening result for an M10 class 8.8 bolt carrying its full tensile capacity, this calculator gives about 4.9 mm (0.5 d) for the bolt threads, and for the internal threads about 3.5 mm in a hardened 800 MPa nut, 7.0 mm (0.7 d) in 400 MPa low-carbon steel, 9.1 mm (0.9 d) in 6061-T6 aluminium and 11.3 mm (1.1 d) in 250 MPa cast iron. The governing value is the larger of the two. Add a safety margin; many shops specify 1 d in steel and 1.5 to 2 d in aluminium or cast iron.

Why does the required engagement depend on the tapped material?

Thread stripping is a shear failure of the weaker of the two threads. The shear area per millimetre of engagement is roughly the same for both threads, so the thread in the lower-strength material strips first. A softer material needs a longer engagement to carry the same load.

How is the thread shear area calculated?

The bolt threads shear on a cylinder at the minor diameter of the internal thread, D1 = d − 1.0825 P, and the width of the bolt thread there is about 0.75 P. The internal threads shear on a cylinder at the major diameter d, where the width of the nut thread is about 0.875 P. Shear area = π × diameter × width fraction × engagement length. The shear strength of the material is taken as 0.6 times its tensile strength.

Does this include the effect of thread tolerances and uneven load sharing?

No. It uses the basic thread profile and an even load share along the engaged length, with a single shear strength factor of 0.6. In a real nut the first few threads carry most of the load, so very long engagements are not proportionally stronger. Use the result as a screening value and add margin.

Should I count the full length of the threaded hole?

No. Only fully formed threads that carry load count. A tapped blind hole also needs a drill depth beyond the engagement for the chamfer and the incomplete threads at the bottom. A common allowance is about three pitches; follow your own hole-drawing standard.

Does this replace a bolted joint calculation?

No. It only checks thread stripping. A bolted joint also needs the bolt preload, clamped parts, embedding, fatigue and the load path to be checked. Use the bolt torque calculator for preload and tightening torque.

Engineering aid for guidance. Basic thread profiles, even load sharing and a 0.6 shear factor; it does not account for thread tolerance classes, thread-forming or inserts, nut dilation, dynamic loads, temperature or corrosion. Verify critical joints against the relevant standard and with your fastener supplier; you remain responsible for the design. Nothing you enter leaves your browser except through a share link you copy yourself.